I think that is supposed to be Senator Leiko. She is essentially one of the main antagonists of Dr-Black-Jack’s “Plus Size” comic series.

In this game, she basically acts like “Freddy” (minus the music of approach). There’s really no other conditions of triggering her except for running out of power. If you’re lucky enough to survive and you’re close to 6am she won’t do much of anything. However, if you’re nowhere near 6am, she will enter the office and jab Mina with a syringe before being transported into what we can assume is like a secret laboratory where Mina is in some sort of tube-like container being force fed with some fattening liquid. Outside the glass (with the phrase “Piggy” scrawled on it) stands the crazed senator overlooking what she has done to Mina.

The "rare" character is one I've personally never seen but a lot of others in the discord have. Basically she functions like Golden Freddy where there's a small chance every time you leave the monitor she'll appear.